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<h1 class="epydoc">Class _Derivative</h1><p class="nomargin-top"><span class="codelink"><a href="numdifftools.core-pysrc.html#_Derivative">source&nbsp;code</a></span></p>
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<pre class="literalblock">
Object holding common variables and methods for the numdifftools

Parameters
----------
fun : callable
    function to differentiate.
n : Integer from 1 to 4 defining derivative order.     (Default 1)
order : Integer from 1 to 4 defining order of basic method used.
        For 'central' methods, it must be from the set [2,4]. (Default 2)
method : Method of estimation.  Valid options are:
        'central', 'forward' or 'backward'.          (Default 'central')
romberg_terms : Number of Romberg terms used in the extrapolation.
        Must be an integer from 0 to 3.                       (Default 2)
        Note: 0 disables the Romberg step completely.
step_fix : If not None, it will define the maximum excursion from step_nom
             that is used and prevent the adaptive logic from working.
             This will be considerably faster, but not necessarily
             as accurate as allowing the adaptive logic to run.
            (Default: None)
step_max  : Maximum allowed excursion from step_nom as a multiple of it. (Default 4)
step_nom  : Nominal step.                          default maximum(x0, 0.02) 
step_ratio: Ratio used between sequential steps in the estimation
             of the derivative (Default 2)
        The steps used h_i = step_nom[i]*step_max*step_ratio**(-arange(steps_num))
step_num : integer
    if not specified it will be set according to the following rules: 
        step_num = 26 if step_fix is None
        step_num = 3.+ np.ceil(self.n/2.) + self.order + self.romberg_terms +4 otherwise
vectorized : True  - if your function is vectorized.
            False - loop over the successive function calls (default).

Uses a semi-adaptive scheme to provide the best estimate of the
derivative by its automatic choice of a differencing interval. It uses
finite difference approximations of various orders, coupled with a
generalized (multiple term) Romberg extrapolation. This also yields the
error estimate provided. See the document DERIVEST.pdf for more explanation
of the algorithms behind the parameters.

 Note on order: higher order methods will generally be more accurate,
         but may also suffer more from numerical problems. First order
         methods would usually not be recommended.
 Note on method: Central difference methods are usually the most accurate,
        but sometimes one can only allow evaluation in forward or backward
        direction.

</pre>

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          <td><span class="summary-sig"><a href="numdifftools.core._Derivative-class.html#__init__" class="summary-sig-name">__init__</a>(<span class="summary-sig-arg">self</span>,
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          <td><span class="summary-sig"><a name="_check_params"></a><span class="summary-sig-name">_check_params</span>(<span class="summary-sig-arg">self</span>)</span><br />
      check the parameters for acceptability</td>
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          <td><span class="summary-sig"><a name="_initialize"></a><span class="summary-sig-name">_initialize</span>(<span class="summary-sig-arg">self</span>)</span><br />
      Set derivative parameters: stepsize, differention rule and romberg 
      extrapolation matrices</td>
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          <td><span class="summary-sig"><a href="numdifftools.core._Derivative-class.html#_fder" class="summary-sig-name" onclick="show_private();">_fder</a>(<span class="summary-sig-arg">self</span>,
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        <span class="summary-sig-arg">f_x0i</span>,
        <span class="summary-sig-arg">x0i</span>,
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      Return derivative estimates of f at x0 for a sequence of stepsizes h</td>
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          <td><span class="summary-sig"><a name="_trim_estimates"></a><span class="summary-sig-name">_trim_estimates</span>(<span class="summary-sig-arg">self</span>,
        <span class="summary-sig-arg">der_romb</span>,
        <span class="summary-sig-arg">errors</span>,
        <span class="summary-sig-arg">h</span>)</span><br />
      trim off the estimates at each end of the scale if not self.step_fix</td>
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          <td><span class="summary-sig"><a name="_derivative"></a><span class="summary-sig-name">_derivative</span>(<span class="summary-sig-arg">self</span>,
        <span class="summary-sig-arg">fun</span>,
        <span class="summary-sig-arg">x00</span>,
        <span class="summary-sig-arg">stepNom</span>=<span class="summary-sig-default">None</span>)</span></td>
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          <td><span class="summary-sig"><a href="numdifftools.core._Derivative-class.html#_fda_mat" class="summary-sig-name" onclick="show_private();">_fda_mat</a>(<span class="summary-sig-arg">self</span>,
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        <span class="summary-sig-arg">nterms</span>)</span><br />
      Return matrix for fda derivation.</td>
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      Generate finite differencing rule in advance.</td>
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      Set the steps to use in derivation.</td>
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          <td><span class="summary-sig"><a href="numdifftools.core._Derivative-class.html#_set_romb_qr" class="summary-sig-name" onclick="show_private();">_set_romb_qr</a>(<span class="summary-sig-arg">self</span>)</span><br />
      Member variables used...</td>
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          <td><span class="summary-sig"><a name="_set_difference_function"></a><span class="summary-sig-name">_set_difference_function</span>(<span class="summary-sig-arg">self</span>)</span><br />
      Set _fdiff function according to method</td>
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          <td><span class="summary-sig"><a href="numdifftools.core._Derivative-class.html#_central" class="summary-sig-name" onclick="show_private();">_central</a>(<span class="summary-sig-arg">self</span>)</span><br />
      Return central difference function</td>
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      Return forward difference function</td>
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      Return backward difference function</td>
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          <td><span class="summary-sig"><a href="numdifftools.core._Derivative-class.html#_romb_extrap" class="summary-sig-name" onclick="show_private();">_romb_extrap</a>(<span class="summary-sig-arg">self</span>,
        <span class="summary-sig-arg">der_init</span>,
        <span class="summary-sig-arg">h1</span>)</span><br />
      Return Romberg extrapolated derivatives and error estimates
    based on the initial derivative estimates</td>
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    <dt>Overrides:
        object.__init__
        <dd><em class="note">(inherited documentation)</em></dd>
    </dt>
  </dl>
</td></tr></table>
</div>
<a name="_fder"></a>
<div class="private">
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">_fder</span>(<span class="sig-arg">self</span>,
        <span class="sig-arg">fun</span>,
        <span class="sig-arg">f_x0i</span>,
        <span class="sig-arg">x0i</span>,
        <span class="sig-arg">h</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="numdifftools.core-pysrc.html#_Derivative._fder">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <pre class="literalblock">
Return derivative estimates of f at x0 for a sequence of stepsizes h

Member variables used
---------------------
n
_fda_rule
romberg_terms

</pre>
  <dl class="fields">
  </dl>
</td></tr></table>
</div>
<a name="_fda_mat"></a>
<div class="private">
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">_fda_mat</span>(<span class="sig-arg">self</span>,
        <span class="sig-arg">parity</span>,
        <span class="sig-arg">nterms</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="numdifftools.core-pysrc.html#_Derivative._fda_mat">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <pre class="literalblock">
Return matrix for fda derivation.

Parameters
----------
parity : scalar, integer
    0 (one sided, all terms included but zeroth order)
    1 (only odd terms included)
    2 (only even terms included)
nterms : scalar, integer
    number of terms

Member variables used
---------------------
step_ratio

</pre>
  <dl class="fields">
  </dl>
</td></tr></table>
</div>
<a name="_set_fda_rule"></a>
<div class="private">
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">_set_fda_rule</span>(<span class="sig-arg">self</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="numdifftools.core-pysrc.html#_Derivative._set_fda_rule">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <pre class="literalblock">

Generate finite differencing rule in advance.

The rule is for a nominal unit step size, and will
be scaled later to reflect the local step size.

Member methods used
-------------------
_fda_mat

Member variables used
---------------------
n
order
method

</pre>
  <dl class="fields">
  </dl>
</td></tr></table>
</div>
<a name="_set_delta"></a>
<div class="private">
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       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">_set_delta</span>(<span class="sig-arg">self</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="numdifftools.core-pysrc.html#_Derivative._set_delta">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <p>Set the steps to use in derivation.</p>
  <p>Member variables used:</p>
  <p>n order method romberg_terms step_fix step_max</p>
  <dl class="fields">
  </dl>
</td></tr></table>
</div>
<a name="_set_romb_qr"></a>
<div class="private">
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       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">_set_romb_qr</span>(<span class="sig-arg">self</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="numdifftools.core-pysrc.html#_Derivative._set_romb_qr">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <pre class="literalblock">

Member variables used
    order
    method
    romberg_terms

</pre>
  <dl class="fields">
  </dl>
</td></tr></table>
</div>
<a name="_central"></a>
<div class="private">
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">_central</span>(<span class="sig-arg">self</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="numdifftools.core-pysrc.html#_Derivative._central">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <pre class="literalblock">
Return central difference function

Member variables used
    n
    fun
    vectorized

</pre>
  <dl class="fields">
  </dl>
</td></tr></table>
</div>
<a name="_forward"></a>
<div class="private">
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       cellspacing="0" width="100%" bgcolor="white">
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  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">_forward</span>(<span class="sig-arg">self</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="numdifftools.core-pysrc.html#_Derivative._forward">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <pre class="literalblock">
Return forward difference function

Member variables used
    fun
    vectorized

</pre>
  <dl class="fields">
  </dl>
</td></tr></table>
</div>
<a name="_backward"></a>
<div class="private">
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">_backward</span>(<span class="sig-arg">self</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="numdifftools.core-pysrc.html#_Derivative._backward">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <pre class="literalblock">
Return backward difference function

Member variables used
---------------------
fun
vectorized

</pre>
  <dl class="fields">
  </dl>
</td></tr></table>
</div>
<a name="_romb_extrap"></a>
<div class="private">
<table class="details" border="1" cellpadding="3"
       cellspacing="0" width="100%" bgcolor="white">
<tr><td>
  <table width="100%" cellpadding="0" cellspacing="0" border="0">
  <tr valign="top"><td>
  <h3 class="epydoc"><span class="sig"><span class="sig-name">_romb_extrap</span>(<span class="sig-arg">self</span>,
        <span class="sig-arg">der_init</span>,
        <span class="sig-arg">h1</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="numdifftools.core-pysrc.html#_Derivative._romb_extrap">source&nbsp;code</a></span>&nbsp;
    </td>
  </tr></table>
  
  <pre class="literalblock">
Return Romberg extrapolated derivatives and error estimates
    based on the initial derivative estimates

Parameter
---------
der_init - initial derivative estimates
h1 - stepsizes used in the derivative estimates

Returns
-------
der_romb - derivative estimates returned
errest - error estimates
hout - stepsizes returned

Member variables used
---------------------
step_ratio - Ratio decrease in step
rombexpon - higher order terms to cancel using the romberg step

</pre>
  <dl class="fields">
  </dl>
</td></tr></table>
</div>
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